By Antonio Arcos, José M. Contreras and María M. Rueda
In this article from the journal Sociological Methods & Research, the authors note that social surveys generally assume that a sample of units (i.e., students, individuals, employees) is observed by two-stage selection from a finite population, which is grouped into clusters (schools, household, companies). This design involves sampling from two different populations: the population of schools or primary stage units and the population of students or second-stage units. Calibration estimators for student statistics can be defined by using combined information based on school totals and student totals, and two calibration estimators for the population total based on unit weights are defined, one at the unit level and one at the cluster level. A simulation study based on two real populations — obtained from the Programme for International Student Assessment database and from the Spanish Household Budget Survey –is carried out to study the empirical performance of this shrinkage estimator.